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Zero-extension convergence and Sobolev spaces on changing domains by Evseev, Nikita; Kampschulte, Malte; Menovschikov, Alexander is a scholarly article available to read on EtoBox.

What is Zero-extension convergence and Sobolev spaces on changing domains about?

We extend the definition of weak and strong convergence to sequences of Sobolev-functions whose underlying domains themselves are converging. In contrast to previous works, we do so without ever assuming any sort of reference configuration. We then develop the respective theory and counterparts to classical compactness theorems from the fixed domain case. Finally, we illustrate the usefulness of these definitions with some examples from applications and compare them to other approaches.

Author

Evseev, Nikita; Kampschulte, Malte; Menovschikov, Alexander

Published

2024

Language

EN